/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | foam-extend: Open Source CFD
   \\    /   O peration     | Version:     4.1
    \\  /    A nd           | Web:         http://www.foam-extend.org
     \\/     M anipulation  | For copyright notice see file Copyright
-------------------------------------------------------------------------------
License
	This file is part of foam-extend.

	foam-extend is free software: you can redistribute it and/or modify it
	under the terms of the GNU General Public License as published by the
	Free Software Foundation, either version 3 of the License, or (at your
	option) any later version.

	foam-extend is distributed in the hope that it will be useful, but
	WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
	General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with foam-extend.  If not, see <http://www.gnu.org/licenses/>.

\*---------------------------------------------------------------------------*/

#include "VectorTemplate.H"
#include "TensorTemplate.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor()
{}


template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor
(
	const VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>& vs
)
:
	VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>(vs)
{}


template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor(const SphericalTensor<Cmpt>& st)
{
	this->v_[XX] = st.ii(); this->v_[XY] = 0;       this->v_[XZ] = 0;
					        this->v_[YY] = st.ii(); this->v_[YZ] = 0;
					                                this->v_[ZZ] = st.ii();
}


template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor
(
	const Cmpt txx, const Cmpt txy, const Cmpt txz,
					const Cmpt tyy, const Cmpt tyz,
					                const Cmpt tzz
)
{
	this->v_[XX] = txx; this->v_[XY] = txy; this->v_[XZ] = txz;
					    this->v_[YY] = tyy; this->v_[YZ] = tyz;
					                        this->v_[ZZ] = tzz;
}


template<class Cmpt>
inline SymmTensor<Cmpt>::SymmTensor(Istream& is)
:
	VectorSpace<SymmTensor<Cmpt>, Cmpt, 6>(is)
{}


// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::xx() const
{
	return this->v_[XX];
}

template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::xy() const
{
	return this->v_[XY];
}

template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::xz() const
{
	return this->v_[XZ];
}

template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::yy() const
{
	return this->v_[YY];
}

template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::yz() const
{
	return this->v_[YZ];
}

template<class Cmpt>
inline const Cmpt&  SymmTensor<Cmpt>::zz() const
{
	return this->v_[ZZ];
}


template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::xx()
{
	return this->v_[XX];
}

template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::xy()
{
	return this->v_[XY];
}

template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::xz()
{
	return this->v_[XZ];
}

template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::yy()
{
	return this->v_[YY];
}

template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::yz()
{
	return this->v_[YZ];
}

template<class Cmpt>
inline Cmpt& SymmTensor<Cmpt>::zz()
{
	return this->v_[ZZ];
}


template<class Cmpt>
inline const SymmTensor<Cmpt>& SymmTensor<Cmpt>::T() const
{
	return *this;
}


// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

template<class Cmpt>
inline void SymmTensor<Cmpt>::operator=(const SphericalTensor<Cmpt>& st)
{
	this->v_[XX] = st.ii(); this->v_[XY] = 0;       this->v_[XZ] = 0;
					        this->v_[YY] = st.ii(); this->v_[YZ] = 0;
					                                this->v_[ZZ] = st.ii();
}



// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //

//- Hodge Dual operator (tensor -> vector)
template<class Cmpt>
inline Vector<Cmpt> operator*(const SymmTensor<Cmpt>& st)
{
	return Vector<Cmpt>(st.yz(), -st.xz(), st.xy());
}


//- Inner-product between two symmetric tensors
template<class Cmpt>
inline Tensor<Cmpt>
operator&(const SymmTensor<Cmpt>& st1, const SymmTensor<Cmpt>& st2)
{
	return Tensor<Cmpt>
	(
		st1.xx()*st2.xx() + st1.xy()*st2.xy() + st1.xz()*st2.xz(),
		st1.xx()*st2.xy() + st1.xy()*st2.yy() + st1.xz()*st2.yz(),
		st1.xx()*st2.xz() + st1.xy()*st2.yz() + st1.xz()*st2.zz(),

		st1.xy()*st2.xx() + st1.yy()*st2.xy() + st1.yz()*st2.xz(),
		st1.xy()*st2.xy() + st1.yy()*st2.yy() + st1.yz()*st2.yz(),
		st1.xy()*st2.xz() + st1.yy()*st2.yz() + st1.yz()*st2.zz(),

		st1.xz()*st2.xx() + st1.yz()*st2.xy() + st1.zz()*st2.xz(),
		st1.xz()*st2.xy() + st1.yz()*st2.yy() + st1.zz()*st2.yz(),
		st1.xz()*st2.xz() + st1.yz()*st2.yz() + st1.zz()*st2.zz()
	);
}


//- Double-dot-product between a symmetric tensor and a symmetric tensor
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor<Cmpt>& st1, const SymmTensor<Cmpt>& st2)
{
	return
	(
		st1.xx()*st2.xx() + 2*st1.xy()*st2.xy() + 2*st1.xz()*st2.xz()
					      +   st1.yy()*st2.yy() + 2*st1.yz()*st2.yz()
					                            +   st1.zz()*st2.zz()
	);
}


//- Inner-product between a symmetric tensor and a vector
template<class Cmpt>
inline Vector<Cmpt>
operator&(const SymmTensor<Cmpt>& st, const Vector<Cmpt>& v)
{
	return Vector<Cmpt>
	(
		st.xx()*v.x() + st.xy()*v.y() + st.xz()*v.z(),
		st.xy()*v.x() + st.yy()*v.y() + st.yz()*v.z(),
		st.xz()*v.x() + st.yz()*v.y() + st.zz()*v.z()
	);
}


//- Inner-product between a vector and a symmetric tensor
template<class Cmpt>
inline Vector<Cmpt>
operator&(const Vector<Cmpt>& v, const SymmTensor<Cmpt>& st)
{
	return Vector<Cmpt>
	(
		v.x()*st.xx() + v.y()*st.xy() + v.z()*st.xz(),
		v.x()*st.xy() + v.y()*st.yy() + v.z()*st.yz(),
		v.x()*st.xz() + v.y()*st.yz() + v.z()*st.zz()
	);
}


//- Inner-sqr of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt>
innerSqr(const SymmTensor<Cmpt>& st)
{
	return SymmTensor<Cmpt>
	(
		st.xx()*st.xx() + st.xy()*st.xy() + st.xz()*st.xz(),
		st.xx()*st.xy() + st.xy()*st.yy() + st.xz()*st.yz(),
		st.xx()*st.xz() + st.xy()*st.yz() + st.xz()*st.zz(),

		st.xy()*st.xy() + st.yy()*st.yy() + st.yz()*st.yz(),
		st.xy()*st.xz() + st.yy()*st.yz() + st.yz()*st.zz(),

		st.xz()*st.xz() + st.yz()*st.yz() + st.zz()*st.zz()
	);
}


template<class Cmpt>
inline Cmpt magSqr(const SymmTensor<Cmpt>& st)
{
	return
	(
		magSqr(st.xx()) + 2*magSqr(st.xy()) + 2*magSqr(st.xz())
					    +   magSqr(st.yy()) + 2*magSqr(st.yz())
					                        +   magSqr(st.zz())
	);
}


//- Return the trace of a symmetric tensor
template<class Cmpt>
inline Cmpt tr(const SymmTensor<Cmpt>& st)
{
	return st.xx() + st.yy() + st.zz();
}


//- Return the spherical part of a symmetric tensor
template<class Cmpt>
inline SphericalTensor<Cmpt> sph(const SymmTensor<Cmpt>& st)
{
	return (1.0/3.0)*tr(st);
}


//- Return the symmetric part of a symmetric tensor, i.e. itself
template<class Cmpt>
inline const SymmTensor<Cmpt>& symm(const SymmTensor<Cmpt>& st)
{
	return st;
}


//- Return twice the symmetric part of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> twoSymm(const SymmTensor<Cmpt>& st)
{
	return 2*st;
}


//- Return the deviatoric part of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> dev(const SymmTensor<Cmpt>& st)
{
	return st - SphericalTensor<Cmpt>::oneThirdI*tr(st);
}


//- Return the deviatoric part of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> dev2(const SymmTensor<Cmpt>& st)
{
	return st - SphericalTensor<Cmpt>::twoThirdsI*tr(st);
}


//- Return the determinant of a symmetric tensor
template<class Cmpt>
inline Cmpt det(const SymmTensor<Cmpt>& st)
{
	return
	(
		st.xx()*st.yy()*st.zz() + st.xy()*st.yz()*st.xz()
	  + st.xz()*st.xy()*st.yz() - st.xx()*st.yz()*st.yz()
	  - st.xy()*st.xy()*st.zz() - st.xz()*st.yy()*st.xz()
	);
}


//- Return the cofactor symmetric tensor of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> cof(const SymmTensor<Cmpt>& st)
{
	return SymmTensor<Cmpt>
	(
		st.yy()*st.zz() - st.yz()*st.yz(),
		st.xz()*st.yz() - st.xy()*st.zz(),
		st.xy()*st.yz() - st.xz()*st.yy(),

		st.xx()*st.zz() - st.xz()*st.xz(),
		st.xy()*st.xz() - st.xx()*st.yz(),

		st.xx()*st.yy() - st.xy()*st.xy()
	);
}


//- Return the inverse of a symmetric tensor give the determinant
template<class Cmpt>
inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st, const Cmpt detst)
{
	return SymmTensor<Cmpt>
	(
		st.yy()*st.zz() - st.yz()*st.yz(),
		st.xz()*st.yz() - st.xy()*st.zz(),
		st.xy()*st.yz() - st.xz()*st.yy(),

		st.xx()*st.zz() - st.xz()*st.xz(),
		st.xy()*st.xz() - st.xx()*st.yz(),

		st.xx()*st.yy() - st.xy()*st.xy()
	)/detst;
}


//- Return the inverse of a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt> inv(const SymmTensor<Cmpt>& st)
{
	return inv(st, det(st));
}


//- Return the 1st invariant of a symmetric tensor
template<class Cmpt>
inline Cmpt invariantI(const SymmTensor<Cmpt>& st)
{
	return tr(st);
}


//- Return the 2nd invariant of a symmetric tensor
template<class Cmpt>
inline Cmpt invariantII(const SymmTensor<Cmpt>& st)
{
	return
	(
		0.5*sqr(tr(st))
	  - 0.5*
		(
		   st.xx()*st.xx() + st.xy()*st.xy() + st.xz()*st.xz()
		 + st.xy()*st.xy() + st.yy()*st.yy() + st.yz()*st.yz()
		 + st.xz()*st.xz() + st.yz()*st.yz() + st.zz()*st.zz()
		)
	);
}


//- Return the 3rd invariant of a symmetric tensor
template<class Cmpt>
inline Cmpt invariantIII(const SymmTensor<Cmpt>& st)
{
	return det(st);
}


template<class Cmpt>
inline SymmTensor<Cmpt>
operator+(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
	return SymmTensor<Cmpt>
	(
		spt1.ii() + st2.xx(), st2.xy(),             st2.xz(),
					          spt1.ii() + st2.yy(), st2.yz(),
					                                spt1.ii() + st2.zz()
	);
}


template<class Cmpt>
inline SymmTensor<Cmpt>
operator+(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
	return SymmTensor<Cmpt>
	(
		st1.xx() + spt2.ii(), st1.xy(),             st1.xz(),
					          st1.yy() + spt2.ii(), st1.yz(),
					                                st1.zz() + spt2.ii()
	);
}


template<class Cmpt>
inline SymmTensor<Cmpt>
operator-(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
	return SymmTensor<Cmpt>
	(
		spt1.ii() - st2.xx(), -st2.xy(),             -st2.xz(),
					           spt1.ii() - st2.yy(), -st2.yz(),
					                                  spt1.ii() - st2.zz()
	);
}


template<class Cmpt>
inline SymmTensor<Cmpt>
operator-(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
	return SymmTensor<Cmpt>
	(
		st1.xx() - spt2.ii(), st1.xy(),             st1.xz(),
					          st1.yy() - spt2.ii(), st1.yz(),
					                                st1.zz() - spt2.ii()
	);
}


//- Inner-product between a spherical symmetric tensor and a symmetric tensor
template<class Cmpt>
inline SymmTensor<Cmpt>
operator&(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
	return SymmTensor<Cmpt>
	(
		spt1.ii()*st2.xx(),
		spt1.ii()*st2.xy(),
		spt1.ii()*st2.xz(),

					      spt1.ii()*st2.yy(),
					      spt1.ii()*st2.yz(),

					                        spt1.ii()*st2.zz()
	);
}


//- Inner-product between a tensor and a spherical tensor
template<class Cmpt>
inline SymmTensor<Cmpt>
operator&(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
	return SymmTensor<Cmpt>
	(
		st1.xx()*spt2.ii(),
					      st1.xy()*spt2.ii(),
					                        st1.xz()*spt2.ii(),

					      st1.yy()*spt2.ii(),
					                        st1.yz()*spt2.ii(),

					                        st1.zz()*spt2.ii()
	);
}


//- Double-dot-product between a spherical tensor and a symmetric tensor
template<class Cmpt>
inline Cmpt
operator&&(const SphericalTensor<Cmpt>& spt1, const SymmTensor<Cmpt>& st2)
{
	return(spt1.ii()*st2.xx() + spt1.ii()*st2.yy() + spt1.ii()*st2.zz());
}


//- Double-dot-product between a tensor and a spherical tensor
template<class Cmpt>
inline Cmpt
operator&&(const SymmTensor<Cmpt>& st1, const SphericalTensor<Cmpt>& spt2)
{
	return(st1.xx()*spt2.ii() + st1.yy()*spt2.ii() + st1.zz()*spt2.ii());
}


template<class Cmpt>
inline SymmTensor<Cmpt> sqr(const Vector<Cmpt>& v)
{
	return SymmTensor<Cmpt>
	(
		v.x()*v.x(), v.x()*v.y(), v.x()*v.z(),
					 v.y()*v.y(), v.y()*v.z(),
					              v.z()*v.z()
	);
}


template<class Cmpt>
class outerProduct<SymmTensor<Cmpt>, Cmpt>
{
public:

	typedef SymmTensor<Cmpt> type;
};

template<class Cmpt>
class outerProduct<Cmpt, SymmTensor<Cmpt> >
{
public:

	typedef SymmTensor<Cmpt> type;
};

template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, SymmTensor<Cmpt> >
{
public:

	typedef Tensor<Cmpt> type;
};

template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, Vector<Cmpt> >
{
public:

	typedef Vector<Cmpt> type;
};

template<class Cmpt>
class innerProduct<Vector<Cmpt>, SymmTensor<Cmpt> >
{
public:

	typedef Vector<Cmpt> type;
};


template<class Cmpt>
class typeOfSum<SphericalTensor<Cmpt>, SymmTensor<Cmpt> >
{
public:

	typedef SymmTensor<Cmpt> type;
};

template<class Cmpt>
class typeOfSum<SymmTensor<Cmpt>, SphericalTensor<Cmpt> >
{
public:

	typedef SymmTensor<Cmpt> type;
};

template<class Cmpt>
class innerProduct<SphericalTensor<Cmpt>, SymmTensor<Cmpt> >
{
public:

	typedef SymmTensor<Cmpt> type;
};

template<class Cmpt>
class innerProduct<SymmTensor<Cmpt>, SphericalTensor<Cmpt> >
{
public:

	typedef SymmTensor<Cmpt> type;
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// ************************************************************************* //
